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What is the approximate percentage value of maximum voltage to its rms value in LCR AC circuit?

Asked in GUJCET 2025 · RMS and mean values

• (1) 22.8%
• (2) 70.7%
• (3) 50%
• (4) 141.4%

Step-by-step solution

Why the other options are wrong

• (1) No route through this physics reaches 22.8%. Between the peak and the rms value of a sinusoid only two ratios exist, √2=1.414 and 1/(√2)=0.707, and 0.228 is neither. Sanity check: (V₀)/(Vᵣₘₛ)=√2, i.e. 141.4%.
• (2) The ratio taken upside down: (Vᵣₘₛ)/(V₀)=1/(√2)=0.707, so 70.7%. The question asks for maximum over rms, which has to come out above 100%.
• (3) Comes from comparing the squares instead of the voltages: (Vᵣₘₛ²)/(V₀²)=1/2=50%. That is the mean value of sin²ω t, the quantity sitting under the square root, not the ratio asked for.

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